Quaternion algebras over elliptic curves

被引：13

作者：

Pumplün, S ^{[1
]}

机构：

[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

来源：

COMMUNICATIONS IN ALGEBRA | 1998年 / 26卷 / 12期

关键词：

D O I：

10.1080/00927879808826415

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

All composition algebras of rank 2 and 4 over elliptic curves are enumerated and partly classified, and examples of octonion algebras are constructed using the generalized Cayley-Dickson doubling process. The underlying field is assumed to be perfect, and of characteristic not two. Some applications are given.

引用

页码：4357 / 4373

页数：17

共 50 条

[1] Quaternion algebras over curves of genus one without rational points
Pumplün, S
ALGEBRA COLLOQUIUM, 2005, 12 (01) : 67 - 92
[2] Algebras associated to elliptic curves
Stephenson, DR
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (06) : 2317 - 2340
[3] On Quaternion Algebras Split by a Given Extension, Clifford Algebras and Hyperelliptic Curves
Darrell Haile
Louis Rowen
Jean-Pierre Tignol
Algebras and Representation Theory, 2020, 23 : 1807 - 1826
[4] On Quaternion Algebras Split by a Given Extension, Clifford Algebras and Hyperelliptic Curves
Haile, Darrell
Rowen, Louis
Tignol, Jean-Pierre
ALGEBRAS AND REPRESENTATION THEORY, 2020, 23 (04) : 1807 - 1826
[5] Nonassociative quaternion algebras over rings
Pumplun, S.
Astier, V.
ISRAEL JOURNAL OF MATHEMATICS, 2006, 155 (1) : 125 - 147
[6] Duality of Heights Over Quaternion Algebras
Christine Liebendörfer
Gaël Rémond
Monatshefte für Mathematik, 2005, 145 : 61 - 72
[7] QUATERNION ALGEBRAS OVER COMMUTATIVE RINGS
TUGANBAEV, AA
MATHEMATICAL NOTES, 1993, 53 (1-2) : 204 - 207
[8] Duality of heights over quaternion algebras
Liebendörfer, C
Rémond, G
MONATSHEFTE FUR MATHEMATIK, 2005, 145 (01): : 61 - 72
[9] Heights and determinants over quaternion algebras
Liebendörfer, C
COMMUNICATIONS IN ALGEBRA, 2005, 33 (10) : 3699 - 3717
[10] Nonassociative quaternion algebras over rings
S. Pumplün
V. Astier
Israel Journal of Mathematics, 2006, 155 : 125 - 147

← 1 2 3 4 5 →